TY - JOUR
T1 - Holomorphic disks and knot invariants
AU - Ozsváth, Peter
AU - Szabó, Zoltán
N1 - Funding Information:
·Corresponding author. E-mail addresses: petero@math.columbia.edu (P. Ozsváth), szabo@math.princeton.edu (Z. Szabó). 1Supported by NSF Grant DMS 9971950 and a Sloan Research Fellowship. 2Supported by NSF Grant DMS 0107792 and a Packard Fellowship.
PY - 2004/8/1
Y1 - 2004/8/1
N2 - We define a Floer-homology invariant for knots in an oriented three-manifold, closely related to the Heegaard Floer homologies for three-manifolds defined in an earlier paper. We set up basic properties of these invariants, including an Euler characteristic calculation, and a description of the behavior under connected sums. Then, we establish a relationship with HF+ for surgeries along the knot. Applications include calculation of HF+ of three-manifolds obtained by surgeries on some special knots in S3, and also calculation of HF+ for certain simple three-manifolds which fiber over the circle.
AB - We define a Floer-homology invariant for knots in an oriented three-manifold, closely related to the Heegaard Floer homologies for three-manifolds defined in an earlier paper. We set up basic properties of these invariants, including an Euler characteristic calculation, and a description of the behavior under connected sums. Then, we establish a relationship with HF+ for surgeries along the knot. Applications include calculation of HF+ of three-manifolds obtained by surgeries on some special knots in S3, and also calculation of HF+ for certain simple three-manifolds which fiber over the circle.
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U2 - 10.1016/j.aim.2003.05.001
DO - 10.1016/j.aim.2003.05.001
M3 - Article
AN - SCOPUS:4243118036
VL - 186
SP - 58
EP - 116
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
IS - 1
ER -